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How to prepare for the difficult PSLE Maths questions

Maths is the language of the universe.

Never has this expression been truer than in today’s technology-dependent world. Being able to speak the language of maths will open up a lot of doors for the child, but in order to prove that they are proficient in that language children first have to successfully pass the PSLE Maths exam.

And some questions from the exam have drawn criticism in the past due to the difficulty level. 

But there is almost no difficulty that cannot be overcome with diligent study and practice.

So, in this article, we will discuss some of the questions from the previous PSLE Maths exams that have been dubbed too difficult and try to find clues that can help your child solve them. 


1. How to help your child prepare for the PSLE Maths exam?

First and foremost, you should be aware of any changes that have been made in that year’s maths syllabus.

You must also find out what the format of the test will be. In general, the PSLE Maths test consists of two papers: Paper 1 and Paper 2

Paper 1 is further subdivided into two booklets (A and B) and children have one hour to finish both booklets. Paper 1 usually doesn’t require any calculations so using calculators is not permitted while working on this part of the exam. 

Scoring high in Paper 1 should be relatively easy if the child has been practicing with the aid of some good PSLE Maths books, is aware of the questions that have been included in the previous years’ exams, has done some mock tests, and isn’t rushing while doing the paper or being careless.

Paper 2 is more difficult and consists of 5 short and 12 long answer questions. The questions are not typically as straightforward as in the previous paper and require some deeper analysis. Calculators are allowed here, however. 

Even though the questions aren’t as straightforward as you would like them to be, do not be intimidated by Paper 2. After all, there is nothing in there that cannot be solved with a bit of determination. 

Although you do need to have a rather strong foundation in maths to successfully tackle all of these questions so make sure that your child knows all the fundamental principles of maths that they are supposed to know.

Since the calculators are permitted your child does not have to waste time doing mental arithmetic in this section, just focus on the analysis. 


2. Finding the appropriate resources.

To practice the tricky questions it is recommended to purchase books that teach children rather advanced mathematical skills, such as advanced modeling or spatial visualization.

Having the appropriate resources is step number one when it comes to exam preparation. Children are also required to utilize their critical thinking skills during the exam so it is recommended to get the resources that focus on the development of that skill. 

Each child has specific strengths and weaknesses and thus how parents can help their children varies as well. Some children may do well just with some practice books, some may require particular learning aids or even the assistance of a private maths tutor

Children also have different learning styles that you can help them use to their advantage. These styles may be auditory (connected to hearing), visual (connected to the sense of sight) or kinaesthetic (connected to the sense of touch). Find out which style benefits your child the most and use it in the PSLE Maths preparation. 

If your child learns better with the auditory aid you can have them read the explanations and the solutions out loud, recite them to your child or have them listen to an online recording (perhaps the ones made by the tutor). 

If your child is a visual learner use various visual aids to help them memorize the material better. These aids may include diagrams and pictures. Creating mental images of the maths problems will help your child recall the necessary information at the actual exam.

Kinaesthetic learners memorize things better by engaging in physical activities, so try arranging those to help your child with the exam preparation. 

Another thing you should keep in mind is that the progress will not occur overnight. In most cases, the child will have to study for several months in order to achieve the desired result.

It is important to nurture a child’s interest in maths during that period.

The children should not end up feeling resentment towards the subject, otherwise, they will have a sense of internal protest during the test preparation period, and this is extremely counterproductive. 

Try creating associations between maths and fun activities in your daily lives. If you have been frequently traveling by car (or indeed any other transport) for several days ask them to calculate how many miles you have traveled in total, and later on, reward them for the correct answer. 

One thing a parent can definitely do to help their child, is try to ease the stress caused by the upcoming test.

Everybody finds exams extremely intimidating and the 12-year-olds are not equipped psychologically to deal with this level of anxiety.

If the child is under the impression that not succeeding at the exam is the end of the world this may have a detrimental effect on them and they may crumble completely on the day of the test.

So, set realistic expectations and encourage your child to be more self-confident. This will serve them better on the exam day and in the long run as well. 


3. Using PSLE maths papers from previous years. 

It is always a good idea to have a look at the exam papers from the previous years.

You can find the papers on the Singapore Examinations and Assessment Board’s (SEAB) website. There you will be able to see the level of difficulty that has been set as well as the maths syllabus for that year. You can also find online test papers to download for free.

When doing a PSLE Maths test from the previous year attempt to create the conditions similar to those in the real exam.

Allot a specific period of time to the exam, do not allow your child to ask you any questions that would reveal the correct answer, and only allow the use of a calculator in the section where it is permitted.

Recreating these exam conditions in your own home will help your child to prepare psychologically for what is expected of them during the real exam.  


4. Several examples of difficult PSLE Maths questions. 

Now let’s have a look at some of the maths questions that students often find difficult.

The first type of question that baffled many students presented them with a set of for triangles increasing in size from left to right.

The triangles were divided by lines that created even smaller triangles within the main figure. Some of the smaller figures were colored gray and some white.

Below the triangles, there was a chart that students needed to fill by counting the total number of internal triangles. In addition to this, they had to calculate the total number of triangles as well as the number of grey and white triangles in the fifth figure which was not presented in the picture. 

The reason students found this question challenging is because it was not similar to any question that was included in the previous years’ PSLE Maths exams.

So this meant that the students could not have practiced for this question.

They needed to rely solely on the knowledge of the mathematical principles and on their critical thinking skills to solve this problem. 

Another question that students found particularly difficult required the use of the elimination process to arrive at the correct answer.

The question was:

"Jack and John made friends with Jill. They want to know when she celebrates her birthday.

Jill gives them 10 different dates. There is a chart of ten dates given in the question. Then Jill tells Jack just the month when she was born, and she tells John the date only.

Jack says that he doesn’t know the date, but he knows that John doesn’t know it either. Whereas John says that at first, he didn’t know when Jill’s birthday was but now he knows. After this Jack says that he now knows it too."

Then the children are asked to figure out the date of Jill’s birthday. 

The reason this question is so challenging is that at first glance it seems illogical. The wordplay in the problem is rather tricky and the child needs to use their creative thinking skills and follow the elimination process in order to get the correct answer. 

This is the type of question even some adults would find confusing, so it is not surprising that many primary 5 students find it too hard to handle as well. 

One more question that gave students and their parents a headache in the 2019 PSLE Maths exam was again connected to the diagram.

It showed five identical semicircles that were arranged along a straight line horizontally (three semicircles on the top and two on the bottom). The spaces between the semicircles were measured and the measurements were given to the students. The question asked students to find the diameter of one circle. 

The reason this question is considered to be difficult, and some may say even inappropriate for the primary school students, is because it requires rather complex analysis and well developed critical thinking skills. Neither of these is common with average primary school students. 

There is more than one way to solve this problem and each requires the knowledge of complex mathematical equations.

The child may also need to draw a model and label all the overlapping lengths. Alternatively, the child may redraw the given figure to complete the circles. 

And the final example of difficult PSLE Maths questions has to do with measuring the distance from one location to the other.

For example, a school and a shop are 120 m apart. They are located between Ben’s home and Susan’s home (there may be a picture given in the question that illustrates the location of the objects).

The school is half-way between the houses. On one occasion Ben and Susan cycled from their houses to the shop. They left their houses at the same time and arrived at the shop at the same time.

Susan was going at the speed of 70m per min. Whereas Ben was cycling 15m more per minute than Susan. 

  1. How much further is Ben’s house from the shop than Susan’s house?
  2. How far is Susan’s house from the shop?

This question is not as straightforward as it first appears.

At first glance, the student may think that Ben cycled 120m more than Susan. However, if you pay close attention and take the distance Susan traveled into consideration as well you will conclude that Ben actually cycled 240m extra. 

This is, of course, not an exhaustive list of all the difficult questions that your child may come across when doing their PSLE Maths test.


5. Do the questions need to be this hard?

These and other difficult questions have been rather controversial in recent years, with many parents and even education professionals claiming that they are unnecessarily hard for this stage of the child’s development.

Meanwhile, others believe that these types of hard questions are necessary for today’s extremely competitive environment as they prepare the students for the difficult challenges they will face in the future. 

Many parents were concerned that the difficulty level of PSLE Maths would shatter the children’s confidence and make them live in a constant state of anxiety.

The minister of education even received an open letter from one mother via Facebook in which she called some maths questions “cruel” and spoke about how the children leave the examination room “crying and deflated”.  

Overall, most people agree that the exam papers should have questions that range in difficulty. And after all, PSLE exam is not the biggest challenge a person will have to face in their lifetime.

So, although scoring 100% on your test would definitely be something to brag about, if a child ends up missing a few (even after all the necessary practice) it is not the end of the world.  

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Tutor City's blog focuses on balancing informative and relevant content, never at the expense of providing an enriching read. 

We want our readers to expand their horizons by learning more and find meaning to what they learn.

Resident author - Mr Wee Ben Sen, has a wealth of experience in crafting articles to provide valuable insights in the field of private education.

Ben Sen has also been running Tutor City, a leading home tuition agency in Singapore since 2010.